Structure Considerations

D. Schulte

2

Luminosity and Parameter Drivers

Beam Quality(+bunch length)

D. Schulte

Luminosityspectrum Beam current

3

Approximate Parameter Derivation

Damping ring and BDS define minimum horizontal beam size at IP

D. Schulte

Not how we chose parameters but how parameters are driven by physics

Beam-beam effects define minimum charge to have full luminosity efficiency

Luminosity efficiency requires structure aperture consistent with minimum charge

Need to maximise RF to beam efficiency and all parameters follow

Long-range Wakefields

• Once bunch charge is fixed main efficiency/current limitation comes from multi-bunch wakefields– Need to ensure stability of jittering beam

• Different criteria– Coherent jitter of the full train

• Expressed by FC

• very likely– Independent jitter of each bunch

• Expressed by FRMS

• Possible– Worst initial pattern

• Expressed by Fworst

• Hopefully not likely

Theoretical Model

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r x f = Ar x 0The final position of the bunches can be expressed as a function of the initial offset

Each complex component of the vectors represents one bunch

Aij depend on the wakefieldsWith no wakefields A=1

Luminosity loss ΔL is proportional to

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ΔL∝r x fr x f*

F gives the increase in luminosity due to long-range wakefields compared to the casewith no long-range wakefield

Example: CLIC_G

FRMS for kick only on the second bunch

Remark: Static ErrorsStatic errors of the main linac structures (scatters) are not very important

Additional Trapped ModeThe importance of a trapped mode depends very much on the frequency

Example: Undamped ModeA mode with 88V/pCm-2 can yield an increase of FRMS by 20%

Steps• Need wakefield in time domain or with a

limited number of modes• Can perform theoretical analysis rapidly• Full simulation will take longer– Are expected to show better stability due to de-

phasing in individual bunches– Do not want to rely on this

First Result• Wakefields at different bunches from Alessandro• Point-like calculation done– FC=O(1012), FRMS=O(1010), Fworst=O(1013)

• Will need to improve the structure– Long long-range wakefield by O(0.1)

• But only envelope given– Change sign of every other kick and things look much

better• Need a real wakefield• Need uncertainty estimates